The rate of a reaction quadruples when temperature changes from 27°C to 57°C.

Question

The rate of a reaction quadruples when temperature changes from \(27^\circ C\) to \(57^\circ C.\) Calculate the energy of activation. 

Given R = 8.314 J \(K^{-1}\) \(mol^{-1}\), log4 = 0.6021 

(1) 38.04 kJ/mol 

(2) 380.4 kJ/mol 

(3) 3.80 kJ/mol 

(4) 3804 kJ/mol

Answer 1

Correct option is (1) 38.04 kJ/mol 

\(\log \left(\frac{k_2}{k_1}\right)=\frac{E_a}{2.303 R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)\)

\( \log \left(\frac{4}{1}\right)=\frac{E_a}{2.303 R}\left(\frac{1}{300}-\frac{1}{330}\right)\)

\(E_a =\frac{(\log (4)) \times 2.303 \times 8.314 \times 300 \times 330}{30} \\\)

\(3.804 \times 10^4 \mathrm{~J} / \mathrm{mol}\)

\(=38.04 \mathrm{~kJ} / \mathrm{mol}\)